Current learning objective

  • -Understand and apply generalized linear models (GLMs) for modeling data with non-normal distributions
  • -Apply GLMs effectively to model binary outcomes (logistic regression) and count data (Poisson or negative binomial regression).
  • Fit, interpret, and assess the adequacy of GLMs

Continuous Distributions

Discrete Distributions

Generalised linear models

Genralised linear models (GLMs) has three components:

  • Assume that Y_i is a member of an exponential family (e.g. Normal/Gaussian, Binomial, Poission, Gamma, etc).
  • A linear predictor \eta_i = \beta_0 + \beta_1 x_{i1} + \ldots + \beta_k x_{ik}.
  • A (smooth and invertible) link function g(\cdot) which transforms the expectation of the response variable \mu_i = E(Y_i) to the linear predictor: g(\mu_i) = \eta_i = \beta_0 + \beta_1 x_{i1} + \ldots + \beta_k x_{ik}.